Skip to main content
SpringerLink
Log in

On Multiresolution Transforms Based on Weighted-Least Squares

  • Chapter
  • First Online:
Advances in Differential Equations and Applications

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 4))

  • 1469 Accesses

Abstract

This work is devoted to construct Harten’s multiresolution transforms using Weighted-Least squares for different discretizations. We establish a relation between the filters obtained using some decimation operators. Some properties and examples of filters are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Amat, S., Donat, R., Liandrat, J., Trillo, J.C.: A fully adaptive PPH multi-resolution scheme for image processing. Math. Comput. Model. 46, 2–11 (2001)

    Article  MathSciNet  Google Scholar 

  2. Aràndiga, F., Cohen, A., Yáñez, D.F.: Learning-based multiresolution transforms with application to image compression. Signal Process. 93, 2474–2484 (2012)

    Article  Google Scholar 

  3. Aràndiga, F., Donat, R.: Nonlinear multiscale descompositions: the approach of A. Harten. Numer. Algorithms 23, 175–216 (2000)

    Article  MATH  Google Scholar 

  4. Aràndiga, F., Yáñez, D.F.: Generalized wavelets design using Kernel methods. Application to signal processing. J. Comput. Appl. Math. 250, 1–15 (2013)

    MATH  Google Scholar 

  5. Burt, P.J., Adelson, E.H.: The Laplacian pyramid as a compact image code. IEEE Trans. Commun. 31, 532–540 (1983)

    Article  Google Scholar 

  6. Getreuer, P., Meyer, F.: ENO multiresolution schemes with general discretizations. SIAM J. Numer. Anal. 46, 2953–2977 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Harten, A.: Multiresolution representation of data: general framework. SIAM J. Numer. Anal. 33, 1205–1256 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  8. Mallat, S.: A Wavelet Tour of Signal Processing. Academic, New York (1999)

    MATH  Google Scholar 

  9. Sweldens, W.: The lifting scheme: a construction of second generation wavelets. SIAM J. Numer. Anal. 29, 511–546 (1998)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

This research was partially supported by Spanish MCINN MTM 2011-22741.

Author information

Authors and Affiliations

  1. Departament de Matemática Aplicada, Universitat de València, C/Doctor Moliner, 46100, Burjassot, Valencia, Spain

    Francesc Aràndiga

  2. Departamento de Matemáticas, Campus Capacitas, CC. NN. y CC. SS. aplicadas a la Educación, Universidad Católica de Valencia, C/Sagrado Corazón, 46110 Godella, Valencia, Spain

    Dionisio F. Yáñez

Authors
  1. Francesc Aràndiga
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dionisio F. Yáñez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dionisio F. Yáñez .

Editor information

Editors and Affiliations

  1. Dept. de Mathemàtiques and IMAC, Universitat Jaume I, Castelló, Spain

    Fernando Casas

  2. Dept. de Mathemàtiques and IMAC, Universitat Jaume I, Castelló, Spain

    Vicente Martínez

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Aràndiga, F., Yáñez, D.F. (2014). On Multiresolution Transforms Based on Weighted-Least Squares. In: Casas, F., Martínez, V. (eds) Advances in Differential Equations and Applications. SEMA SIMAI Springer Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-06953-1_13

Download citation

Publish with us

Policies and ethics

Search

Navigation